Fundamentals of Missing Data in Evaluation

Presentation to MSU Department of Psychology, Program Evaluation Occasional Speaker Series, East Lansing, MI

Steven J. Pierce

pierces1@msu.edu

Center for Statistical Training and Consulting

2024-12-05

Outline

What is missing data?
Why do we end up with missing data?
Why should we care about missing data?
How can we diagnose the missing data issues for a given study?
What should we do about missing data?

What is missing data?

Missing data (MD) are measurements you want or intended to collect but did not get.^[1]

Having MD is common in research & evaluation studies.
If you do much evaluation work, you will run into MD.

Why do we end up with missing data?

Data collection doesn’t always go according to plan…

Human Factors	Other Factors
Participant behavior	Equipment failures
Evaluator errors	Records/Databases
Partner behavior	Unusual Events

Why do we end up with missing data? Like many things in life, data collection doesn’t always go according to plan.

> Human factors often contribute to the occurrence of missing data. For example, a survey participant may skip a question without recording any response, offer an illegible or irrelevant answer, refuse to answer it, or simply say “I don’t know”. They may skip whole instruments or entire data collection visits. But evaluators occasionally make errors that lead to missing data. Imagine forgetting to take a data collection form with you, or programming the skip pattern for an online survey incorrectly. Sometimes, our evaluation partners’ decisions or behavior can prevent obtaining some data we wanted. Perhaps they object to sharing something with you, or were not diligent about logging some events of interest.

Other things can go wrong too. Perhaps a physical instrument breaks, or its battery dies, or your online survey app crashes. If you’re using an organization’s records or databases, those may be incomplete, difficult to search for relevant data, coded in unhelpful ways, or could have been lost or damaged or even destroyed according to some retention policy. In terms of events, consider the recent hurricanes in Florida that disrupted data collection for one of my projects.

Missing Data & Project Lifecycle

Why should we care about missing data?

Ethics for Evaluators

Handling missing data well enacts our guiding principles^[2]:

AEA logo.

Systematic inquiry
Competence
Integrity

Perhaps the broadest answer to why we should care about missing data is that this is an ethics issue. Thoughtful handling of missing data is a good way to enact several of AEA’s guiding principles for evaluators.

> Systematic inquiry demands that we examine the quality of the available data and use it appropriately. We have an obligation to use sound methodology. There are scientific consequences of missing data but there are also legitimate, evidence-based methods for minimizing its impact on our analyses, conclusions, and products.
> Competence demands that we invest in skills necessary to understand and handle missing data properly because doing it poorly may compromise our evaluations. Our funders, clients, and stakeholders–including the program staff and the people and communities they serve and operate within–need and deserve competent evaluation services.
> Integrity demands that we be transparent about the amount of missing data, how we handled it, and how it may affect our evaluation results.

Scientific Activities^[3]

There are 3 major scientific activities that can be affected by missing data.

Making structured observations of constructs.
Using observations to draw inferences about relationships between constructs.
Generalizing the results to populations beyond the collected sample.

Consequences for Measurement^[3]

Availability of constructs
Decreased reliability due to increased error variance
Bias from poor content coverage
Construct validity

Missing data can affect the availability of a construct for your analyses. The extreme case would be a construct measured by a single variable. If that’s missing, then the entire construct is missing for that individual and it may be very difficult to recover that information. Missing data is still a problem when we use multiple indicators to measure a construct, though perhaps less severe, and it may depend on how you combine items to create the score.

Missing data decreases the reliability and construct validity of our measures. Internal consistency reliability decreases because missing data increases the error variance in a measure. You may recall that reliability is a function of how many items are used, so fewer observed items leads to lower reliability.

Further, some items may be more important indicators of a construct than others. You may get a biased estimate of the construct due to poorer content coverage if they are missing. Construct validity depends on both reliability and content coverage, so missing data is a threat to construct validity.

Consequences for Internal Validity^[1,3]

Selection bias
Compromised randomization
Power and precision
Inaccurate model assumptions

Missing data is a threat to a study’s internal validity for several reasons. Selection bias can result from systematic differences between subgroups of participants on constructs relevant to the study conclusions. For example, those subgroups could be treatment versus control groups, people who complete the study versus drop out, or those who have complete data versus incomplete data. These differences may manifest with respect to demographic variables, covariates, predictors, mediators, moderators, or outcomes. Imagine evaluating a longitudinal health study where people who start out with worst symptoms drop out before the posttest more often than those with mild symptoms. Dropping out leads to missing data at posttest. If we fail to handle that properly in the analysis, we may draw inaccurate conclusions about the longitudinal trend in outcome scores. Or perhaps the retention rates differ between treatment and control groups in that same study. Selection bias from such differences reduce the sample representativeness and become rival explanations for findings, making them a threat to internal validity.

We use randomization to make groups equivalent on measured and unmeasured confounding variables as a way to strengthen validity. That works best in large samples. However, missing data can compromise that effect of randomization by reducing sample size. It can also reduce randomization’s ability to achieve equivalence between groups on confounding variables when data are missing differentially across the groups. That reduces internal validity.

Most statistical software defaults to listwise deletion of cases that have any missing values on the variables involved in an analysis. Reducing the sample size will always reduce both power to detect effects and the precision of effect size estimates. In addition to reducing overall sample size, missing data may lead to more unbalanced sample sizes between groups in a study, which also reduces statistical power in many models.

Finally, missing data can change the distributions of variables in ways that invalidate the assumptions of various statistical models. Some models are more robust than others, but making inaccurate modeling assumptions risks running analyses that will yield misleading conclusions. That’s another threat to internal validity.

Consequences for Generalizability^[1,3]

A representative sample is crucial to generalizing to the intended population!

Theory development & cumulative knowledge
Policy & decision-making

We draw samples to study populations when it isn’t feasible to collect the data we want from the entire population. The key to getting inferences that properly generalize from a sample to the intended population is getting a representative sample. Biases creep into findings when we use non-representative samples. Missing data can introduce systematic biases into our samples. Suppose you’re studying a behavior that’s illegal or stigmatized in some way. Some people who engage in it may be reluctant to provide all the data you want. If we ignore the missing data problem, listwise deletion will result in analyzing the subset of the intended population that’s willing to answer our questions. That in effect changes the population to which we could legitimately generalize our findings from “people who engage in behavior x” to “people who engage in behavior x and provided complete data”. Many people fail to attend to that though and assume their results still apply to the original intended population.

That has consequences for developing and testing scientific theories and accumulating knowledge across studies. An example is the effect of publication bias, also called the file drawer problem, on meta-analyses. We know that studies with non-significant findings are less likely to get published. That means the published literature has a missing data problem that can seriously distort the results of meta-analyses that aim to summarize results of a collection of published papers.

Finally, the big picture here is that when missing data impair generalizability, we may be using inaccurate or misleading findings to inform public policy and important decisions.

How can we diagnose the missing data issues for a given study?

Cattell’s Data Box^[4]

How much data is there? Data volume is \(N_{values} = P \times V \times T\)

Slices through the cube represent subsets of data.
Constructs are often measured by groups of adjacent variables (items).
Missing data puts holes in your cube!

Raymond Cattell described data as forming a 3-dimensional box or cube, with the dimensions being persons, variables, and occasions (or times). This is useful for thinking about the total volume of data we aim to collect. At least for a simple longitudinal study where we collect the same instruments for each person at each time point, we can just multiply the number of desired participants by the number of variables by the number of time points to get the number of desired data values, which is the volume of the cube. Different slices through the cube represent specific subsets of data. The top layer would be all the data for a given person (all variables at all time points). The left-most vertical slice would be all the data for a specific variable across all persons and time points. The front face of the cube would be time 1 data on all variables for all persons. We could further refine this idea by recognizing that constructs are often measured by groups of adjacent variables (items).

Missing data puts holes in the cube, turning it into something like Swiss cheese. The impact of that depends on how much data volume is lost and any patterns in where and why those holes are located relative to the data you want to analyze.

Types of Missingness^[3,5]

Item level
Construct level
Person level (unit non-response)
Person-period level (wave nonresponse; intermittent vs. dropout)

There are a variety of types of missingness to consider as we begin describing a given data set. One place to start involves examining different parts of the data cube. For example, item-level missingness pertains to an individual variable. What percentage of its values are missing? Contrast that with construct-level missingness, which is when an entire construct is missing. Some scoring methods leave a construct missing if any of its items are missing, others may still yield a score despite some missing items. Construct missingness is usually a bigger problem than item-level missing data.

Person-level missing data, some times called unit nonresponse, is when all the data for a person is missing. Refusing to participate will usually cause person-level missing data. That’s an extreme example, but a related type of missingness happens at the person-period level when a participant skips an entire data collection event. That’s also called wave non-response. It affects all constructs collected at that time point. In longitudinal studies, person-period missingness could be intermittent, with a participant skipping one event but returning for subsequent events, or it may be a result of dropout or attrition that affects all remaining time points.

Describing the Amount of MD^[3,6]

Report numbers & percentages of:

Participants w/ any data at each time point (retention/attrition)
Complete vs. incomplete cases (overall & by time point)
Missing values for each variable & construct
Reasons for attrition/dropout and other missing data

Use a Good Tracking System

Track attendance at data collection events & participants’ exit from the study.

The dimensions of Cattell’s data box suggests some obvious summaries of the amount of missing data. For example, we probably want to examine and report the number and percentage of participants in the study who have any data at each time point and use that to examine retention or attrition rates. Then we can go further and report the number of complete vs. incomplete cases, both overall and separately by time point. Then, we can compute the numbers and percentages of missing values for each variable, both overall and separately by time point.

Finally, it can be really useful to report on the reasons why participants drop out, skip data collection events, or have other missing data.

> All of these things get easier when you have a tracking system that records:

Whether & when participants attended data each collection event
When & why participants exit the study

Patterns of Missing Data^[5]

Y: matrix of all the values that could be observed
Y_obs: subset of Y values that end up observed
Y_miss: subset of Y values that end up missing
R: response matrix of dummy-coded missingness indicators showing which Y values are observed (0, part of Y_obs) vs. missing (1, part of Y_miss)

Tip

We can aggregrate and visualize R to describe patterns of missingness!

Example Patterns of Missing Data

Missingness patterns for Dutch boys growth study data (748 boys, 9 variables, 1 time point)^[7]

This is graph summarizes data from a developmental study about growth in 748 Dutch boys. The variables include age, region, weight, height, body mass index, head circumference, and three measures of pubertal development. This is just a convenient dataset because it comes with an R package that I use to deal with missing data. The graph illustrates what I mean by missing data patterns. Each row in the graph represents a distinct pattern of observed versus missing values across the whole set of variables. The left side is annotated with the number of boys showing each pattern, the right side tells you how many missing values there are on that row, and the bottom shows the total number of missing values for each variable. With 748 boys and 9 variables, there should be 6732 values, but we can see at the bottom that 1622 (24%) are missing. So this data box has a lot of holes in it.

The first row shows 223 boys have complete data: that’s about 30% of the sample. So, 70% of them have at least one missing value. We can also see that the most common pattern is that 437 boys have missing data for the 3 pubertal development measures, but observed data on all the other measures. That’s 58% of the sample.

Another thing we can see here is that body mass index is always missing whenever either height or weight is missing. That’s because BMI is a measure derived from both height and weight. That’s construct missingness caused by item-missingness.

Rubin’s Mechanisms of Missingness^[8]

Missing completely at random (MCAR)
Missing at random (MAR)
Missing not at random (MNAR)

Impact on Statistical Results^[3]

Some mechanisms yield more bias: MCAR < MAR < MNAR

Understanding Donald Rubin’s system for classifying missing data is crucial to making good decisions about how to handle missing data. This system is pervasive in the literature on missing data because it’s useful despite reliance on some unintuitive names. Rubin defined three categories, each referring to the probability of missing values given information about the variables with missing data, other covariates, and a hypothetical mechanism that causes the missing data. The three categories are:

Missing completely at random (MCAR)
Missing at random (MAR)
Missing not at random (MNAR)

> These three mechanisms affect the amount of bias missing data causes in statistical analyses, with MCAR yielding the least bias and MNAR yielding the most. Let’s take a closer look at each mechanism.

MCAR

MCAR is when neither observed nor unobserved values predict which values are missing.

MAR

MAR is when observed values predict which values are missing.

MNAR

MNAR is when unobserved values predict which values are missing.

MNAR is sometimes called non-ignorable nonresponse^[5]. That’s because under this mechanism whether or not a value is missing depends on unobserved values, either on the variable itself, or on other unobserved variables. There are hidden patterns to the missingness that we can’t easily account for in our analyses. That leads to potentially serious biases in our results. One challenge is that we can’t prove our data is MNAR without actually obtaining the data that are missing. However, if we can get that, then we wouldn’t even have missing data anymore. You may be able to make logical arguments for why we might expect data to be MNAR in a specific study, but other scientists may or may not be persuaded by those arguments when you can’t provide supporting evidence due to lack of the necessary data.

Rubin’s Mechanisms & Cattell’s Box^[3,4,8]

Classifying large datasets according to Rubin’s mechanisms is messy.

Subsets of the data may fit into different mechanisms
Classify mechanisms for meaningful subsets of data defined by dimensions of the data box (persons, variables, times)^[3]

Predictors of Missingness in Longitudinal Studies

Study arms and/or sites
Baseline/pretest values of outcome variables
Other covariates (demographics)

Tip

Consider predictors of person, item, construct, and person-period missingness. Think carefully about your study context and data to look for meaningful, sensible things to test when evaluating missing data issues.

Because we can’t prove that our missing data is MNAR, one of the key tasks is differentiating between data that are MCAR and MAR. The obvious way to do that is to run some analyses to look at whether you can predict which values are missing. Here are some examples of analyses you might use in various situations to identify which missingness mechanism applies to your data.

If you have a study with multiple arms (that is groups, like intervention and control) or sites, consider compring consent and attrition rates between them. If more people are differentially consenting or dropping out of one arm or site, then that variable predicts missingness and you have at best a MAR situation.

Another possible predictor of missingness at later time points is the pretest value of the longitudinal outcome measure. Depending on the outcome, maybe people with unusually high or low scores are more likely to end up with missing data later on.

Of course, demographics and other covariates may also be predictors of missing data.

> So the take away here is that your initial data analysis needs to consider testing for predictors of missingness. That may be a matter of predicting either person-level non-response (refusal to participate), item or construct-level missingness, or person-period missingness, such as attrition or intermittently skipping data collection events. Finding predictors of missingness means that you have a MAR situation.

What should we do about missing data?

Prevention^[3,9,10]

“An ounce of prevention is worth a pound of cure.” (Benjamin Franklin, 1735)

The amount of missing data affects its potential impact on the study
Design your study to reduce the amount of missing data

As the old adage says, “An ounce of prevention is worth a pound of cure.” This absolutely applies to handling missing data problems.

Statistical methods for analyzing incomplete datasets are great, but using them requires knowledge, skill, software, time, and effort. The size and complexity of the missing data problem is directly related to its potential impact on your study and what it will take to solve that problem.

Fortunately, good study design can help evaluators reduce the probability and amount of missing data, thereby reducing its potential impact on measurement, internal validity, and generalizability. The prevention suggestions I’m going to share are by no means an exhaustive list; I just want you to recognize that prevention is your first, and possibly best, opportunity to handle missing data problems.

Prevention: Data Collection Frequency & Timing^[3]

Frequent data collection with short intervals between events is burdensome
Collect longitudinal data at sensible times given expected temporal patterns

First, let’s consider fine-tuning data collection logistics. When participants have to put effort into responding, frequent data collection at short intervals increases their burden. That risks decreasing their motivation and the effort put into any given response, which could cause item, construct, or wave non-response, or even lead to dropout.

While having rich longitudinal data is good for modeling, it is better to have more complete data collected at the right times than to have many time points. Often we have an idea about the temporal patterns of change that we expect, so focus on the critical periods that enable you to see the key aspects of longitudinal trajectories. Collect more often during periods where you expect rapid change and less often when expect relative stability or slower change.

Prevention: Number of Variables^[3,9,10]

Every variable is an opportunity for missing data.

Only collect variables that you need
Choose instruments wisely (short, reliable, valid, & relevant)
Consider collecting multiple measures of key constructs

Remember that every variable you try to collect adds to participant burden. Asking for too much risks tiring, frustrating, boring, or irritating people in ways that lead to missing data.

You can reduce missing data problems by only collecting variables you need. You should know why you need each variable or instrument. Similarly, you should choose instruments wisely: pick things that are short, reliable, and valid whenever possible. Making sure their relevance is clear to participants may also help because people may be more likely to skip things they think are irrelevant or offensive.

On the other hand, there is a case for strategically collecting multiple measures of key constructs. Different measures of a construct are often correlated and that can help you if data for one are incomplete but another is complete. Relationships between measures can be used to recover some of the missing information when modeling incomplete datasets.

Prevention: Dropout^[3,9–11]

Establish relationships
Maintain contact with participants
Offer adequate incentives
Make participation convenient

Timing should be ~33-34 min by here. Dropout is a major cause of missing data in longitudinal studies, but there are some strategies you can use to minimize it. I’ll describe some strategies we use on an evaluation of EFNEP, a federal nutrition education program for low-income people.

We partner with local organizations to find participants, so establishing good relationships with them means they sometimes help us keep participants engaged.

Another key strategy is maintaining contact with particpants. We use reminder postcards, text messages, and phone calls to encourage people to attend the follow-up data collection events. Even if someone skips the 6-month event we still invite them to the 12 month event unless they explicitly withdraw from the study because intermittent wave non-response is better than complete dropout.

We also aim to offer people adequate incentives to participate. We pay participants promptly for each data collection event, with the amounts increasing over time.

Finally, we make data collection convenient by scheduling events at locations and times that are easy for groups of participants to attend. Sometimes we have to schedule extra sessions. We send multiple data collectors to each session so it runs efficiently and reduces how much time participants have to spend. For some groups, we use translated instruments and staff that speak Spanish to better engage participants in their primary language.

Prevention: Data Collection Methods

Develop detailed protocols
Train data collection & entry staff
Pay attention to instrument design
Test equipment & instruments

Because data collection is essential to evaluation projects, we need to develop detailed protocols that will maximize data quality. Study protocols should anticipate the possibility of missing data and include elements that may prevent it. For example, make checklists of the materials required for each data collection event and review it in advance of each one. If you’re administering print surveys in a group setting, check each one for skipped items or sections as it’s handed in while there’s still a chance for the participant to respond. If you’re using an online survey, program it to notify participants when they skip something and give them the option to either fill it in or proceed anyway. Say you’re going to observe a classroom setting. Consider using multiple observers and structured forms for recording data. Make sure the behaviors to be recorded are clearly defined. Keep observation sessions short enough to avoid fatigue and inattention. Similar ideas apply if you’re going to review documents or abstract data from records: use multiple staff, structured forms, and clear definitions.

Train the data collection staff on the protocols and get them to practice before collecting real data if possible. For data entry, plan a review process and give staff performance feedback. Consider using double-entry and reconciling discrepancies between the data entered by 2 different staff.

Poorly designed instruments may increase the rate of missing data. Pay close attention to instrument design. Make sure instructions and wording are clear, layout is readable, response options make sense, and generally follow principles of good survey design. Pilot test the instruments.

Make sure you test equipment regularly, have spare devices, cords, or batteries in case one fails. Make sure staff know how to use the equipment. If you’re using online data collection tools, test skip patterns carefully before starting data collection.

Treatment: Traditional Methods^[3,12]

Data Deletion	Single Imputation
Listwise deletion	Mean Substitution
Pairwise deletion	Hot-Deck Imputation
Available Items Analysis	Regression Imputation
	Last Observation Carried Forward

Timing should be ~37-38 min by here. Despite effective prevention measures, you’re still likely to end up with some missing data. A variety of traditional methods for handling missing data have been used and discussed in the literature. This table lists examples of two types of approaches to the problem: data deletion methods and single imputation methods.

The deletion-based methods are flawed because they inefficiently use the data. Discarding data you’ve spent resources collecting is wasteful.

Listwise deletion drops every case that has missing data on any variable in the analysis. That’s perhaps the most commonly used method because it is the default behavior for many statistical software packages. It can only give you unbiased parameter estimates if the data are MCAR and you still lose power due to shrinking sample size. But MCAR is a rare situation. You’re far more likley to have MAR, and then using listwise deletion will give you biased results in addition to low power. If there are high rates missingness and many different patterns of missingness, you may not end up with enough observations to do meaningful analyses.

Pairwise deletion uses all available data by only eliminating data at the variable level instead of the person level. In a correlation matrix, pairwise deletion allows sample size to vary depending on which variables you’re correlating. That preserves more power, but is still only unbiased under MCAR and it causes other problems. For example, different subsets of cases may be used for each variable. That can lead to problems with standard errors.

The available items method is used when combining multiple items to measure constructs. If you’ve got a 6 item-scale for depression but only 4 items are complete, you might take the mean of those 4 and use that as the scale score. This makes strong assumptions about the interchangeability of items and about the factor structure. It may decrease the variance between items and will often decrease reliability.

Single imputation methods represent various approaches to replacing each missing value with a single guess about what value should be there. They fill the holes in the original, incomplete dataset to create a complete, imputed dataset. For example, one might swap in the overall mean or a group mean for a variable, or use the hot deck method to swap in the observed value from an randomly selected but otherwise similar case. In longitudinal studies, sometimes people handle dropout by carrying the last observed value forward to future time points. Meanwhile, regression imputation uses complete variables to predict the values of incomplete variables, then replaces the missing value with the conditional mean of the missing variable given the observed predictors.

Statisticians have identifed limitations and flaws for all single imputation methods. While they increase power relative to deletion methods and there are some narrowly defined circumstances when they work reasonably, the single imputation methods make untenable assumptions, generally produce biased estimates even under MCAR and MAR mechanisms, and underestimate standard errors.

Fortunately, there are better, more modern methods available that don’t suffer the drawbacks of these traditional methods.

Treatment: Modern Methods^[3,12]

Full-information maximum likelihood (FIML) estimation
Multiple imputation (MI)

Treatment: FIML^[3,12]

FIML estimates parameters by combining observed data, relationships among observed variables, and assumptions about distributions.

Seeks parameter estimates that best fit the data
Uses all available data without imputing any values
Benefits from auxilliary variables
Works well with MCAR and MAR
Yields biased estimates under MNAR
Available in structural equation modeling (SEM) software

Let’s take a closer look at the FIML method. It estimates parameters by combining observed data, relationships among observed variables, and assumptions about distributions. It seeks the combination of parameter estimates that best fit the overall dataset, which are the ones that make the observed data most likely given the model assumptions. The FIML computations take advantage of all the available data from each case, whether it is complete or incomplete without imputing any of the missing values.

FIML benefit from adding auxiliary variables to the model that either predict missingness or are correlated with the incomplete variables. They provide a way to recapture some of the information lost due to missing data. Auxiliary variables are more useful when they’re mostly complete and at least modestly correlated with the incomplete variables, say around r = 0.40.

FIML is unbiased and yields accurate standard errors under both MCAR and MAR mechanisms, but of course can’t fully solve the missing data problem under MNAR, though it does better than traditional methods.

If you want to use FIML methods, look in structural equation modeling software. Many familiar models–such as regression, ANOVA, and mixed models–can be translated into the SEM framework, which makes FIML reasonably accessible.

Treatment: MI^[3,6,12]

MI replaces each missing value with m indpendent draws from the variable’s conditional distribution.

Uses all available data
Requires both imputation & analysis models
Pools estimates across analyses of m imputed datasets
Preserves uncertainty associated with imputation
Quantifies influence of missing data
Works well with MCAR and MAR
Can handle data that are MNAR

Multiple imputation replaces each missing value with several independent draws from the variable’s conditional distribution, leaving us to pool the results of analyzing m complete, imputed datasets. It uses all the available data along the way. The process requires building two different models. First you create an imputation model that uses relationships between variables to predict the values of incomplete variables given observed values from each case. As in FIML, the imputation model benefits from adding auxiliary variables that either predict missingness or are correlated with the incomplete variables. They facilitate recapturing some of the information lost due to missing data. The imputation model must contain effects that will be in the analysis model to perform well and obtain the conditional distributions used to draw good imputed values. The analysis model must reflect your hypotheses, using predictors and covariates to predict the outcome variables. It must be run on each imputed dataset. Pooling the parameter estimates across the set of analysis models gives you the final estimates while properly reflecting the uncertainty associated with replacing missing data with imputed values. Pooling also offers a unique advantage of MI over other methods: it quantifies the influence of missing data on parameter estimation. No other method offers that option.

MI is unbiased and yields accurate standard errors under both MCAR and MAR mechanisms, and it can even handle MNAR data reasonably in some circumstances.

Where to Learn More

Short overviews^{[1,5,13–16]}
Some good textbooks^[3,6,12,17]
Preventing missing data in:
- Clinical studies^[10]
- Longitudinal studies^[11]
- Surveys^[9]
Dealing with item-level missingness in scale scores^[14,16]

Software Tools

SPSS: check out the MVA and MULTIPLE IMPUTATION syntax commands
R packages: see the CRAN Task View on Missing Data
Both FIML and MI are supported by Mplus and the R package lavaan

References

1. Fernández-García, M. P., Vallejo-Seco, G., Livácic-Rojas, P., & Tuero-Herrero, E. (2018). The (ir)responsibility of (under)estimating missing data. Frontiers in Psychology, 9(556). https://doi.org/10.3389/fpsyg.2018.00556

2. American Evaluation Association. (2018). Guiding principles for evaluators [Web Page]. Author. https://www.eval.org/About/Guiding-Principles

3. McKnight, P. E., McKnight, K. M., Sidani, S., & Figueredo, A. J. (2007). Missing data: A gentle introduction. Guilford Press.

4. Cattell, R. B. (1966). The data box: Its ordering of total resources in terms of possible relations systems. In R. B. Cattell (Ed.), Handbook of multivariate experimental psychology (pp. 67–128). Rand McNally.

5. Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Bulletin, 7(2), 147–777. https://doi.org/10.1037//1082-989X.7.2.I47

6. van Buuren, S. (2018). Flexible imputation of missing data (2nd ed.). Chapman & Hall/CRC Press. https://doi.org/10.1201/9780429492259

7. Fredriks, A. M., Buuren, S. van, Burgmeijer, R. J. F., Meulmeester, J. F., Beuker, R. J., Brugman, E., Roede, M. J., Verloove-Vanhorick, S. P., & Wit, J.-M. (2000). Continuing positive secular growth change in the netherlands 1955-1997. Pediatric Research, 47, 316–323. https://doi.org/10.1203/00006450-200003000-00006

8. Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581–592. https://doi.org/10.1093/biomet/63.3.581

9. Leeuw, E. D. de. (2001). Reducing missing data in surveys: An overview of methods. Quality & Quantity, 35(2), 147–160. https://doi.org/10.1023/A:1010395805406

10. Wisniewski, S. R., Leon, A. C., Otto, M. W., & Trivedi, M. H. (2006). Prevention of missing data in clinical research studies. Biological Psychiatry, 59, 997–1000. https://doi.org/10.1016/j.biopsych.2006.01.017

11. Laurie, H. (2008). Minimizing panel attrition. In S. Menard (Ed.), Handbook of longitudinal research (pp. 167–184). Academic Press.

12. Enders, C. K. (2022). Applied missing data analysis (2nd ed.). Guilford Press. https://www.appliedmissingdata.com

13. El-Masri, M. M., & Fox-Wasylyshyn, S. M. (2005). Missing data: An introductory conceptual overview for the novice researcher. Canadian Journal of Nursing Research, 37(4), 156–171.

14. Graham, J. W. (2009). Missing data analysis: Making it work in the real world. Annual Review of Psychology, 60, 549–576. https://doi.org/10.1146/annurev.psych.58.110405.085530

15. Little, T. D., Jorgensen, T. D., Lang, K. M., & Moore, E. W. (2014). On the joys of missing data. Journal of Pediatric Psychology, 39(2), 151–162. https://doi.org/10.1093/jpepsy/jst048

16. Newman, D. A. (2014). Missing data: Five practical guidelines. Organizational Research Methods, 17(4), 372–411. https://doi.org/10.1177/1094428114548590

17. Graham, J. W. (2013). Missing data: Analysis and design. Springer. http://link.springer.com/openurl?genre=book&isbn=978-1-4614-4017-8

Fundamentals of Missing Data in Evaluation

Outline

What is missing data?

Why do we end up with missing data?

Missing Data & Project Lifecycle

Why should we care about missing data?

Ethics for Evaluators

Scientific Activities[3]

Consequences for Measurement[3]

Consequences for Internal Validity[1,3]

Consequences for Generalizability[1,3]

How can we diagnose the missing data issues for a given study?

Cattell’s Data Box[4]

Types of Missingness[3,5]

Describing the Amount of MD[3,6]

Patterns of Missing Data[5]